Posts tagged 'second-apotome'

G.456 second apotome

But if the annex be:term:commensurable <G.372> in length with the:term:rational <G.392>segment set out, and the:term:square <G.63> on the whole be greater than that on the annex by the square on a segment commensurable with the whole, let the apotome be called a:term:**second apotome** <second-apotome>.

G.457 medial segment there

If from a medial segment there be subtracted a medial segment which is commensurable with the whole in square only, and which contains with the whole a medial rectangle, the remainder is irrational; and let it be called a second apotome of a medial segment.

G.463 apotome medial segment

To a second apotome of a medial segment only one medial segment can be annexed which is commensurable with the whole in square only and which contains with the whole a medial rectangle.

G.468 find the second apotome

Find the second apotome.

G.478 area contained rational

If an area be contained by a rational segment and a second apotome, the “side” of the area is a first apotome of a medial segment.

G.479 area contained rational

If an area be contained by a rational segment and a third apotome, the “side” of the area is a second apotome of a medial segment.

G.484 square apotome medial

The square on a first apotome of a medial segment applied to a rational segment produces as breadth a second apotome.

G.485 square apotome medial

The square on a second apotome of a medial segment applied to a rational segment produces as breadth a third apotome.

G.495 medial area rational

If from a medial area a rational area be subtracted, there arise two other irrational segments, either a first apotome of a medial segment or a segment which produces with a rational area a medial whole.

G.496 medial area there

If from a medial area there be subtracted a medial area incommensurable with the whole, the two remaining irrational segments arise, either a second apotome of a medial segment or a segment which produces with a medial area a medial whole.